#include <iostream>
#include <vector>
#include <string>
#include <stack>
#include <queue>
#include <unordered_set>
#include <unordered_map>
#include <functional>
#include <cmath>
#include <cstring>
#include <algorithm>
#include <set>
using namespace std;

// 作者：灵茶山艾府
// 链接：https://leetcode.cn/problems/minimum-reverse-operations/solutions/2204092/liang-chong-zuo-fa-ping-heng-shu-bing-ch-vr0z/
// 来源：力扣（LeetCode）
// 著作权归作者所有。商业转载请联系作者获得授权，非商业转载请注明出处。
class Solution
{
public:
    vector<int> minReverseOperations(int n, int p, vector<int> &banned, int k)
    {
        unordered_set<int> ban{banned.begin(), banned.end()};
        set<int> sets[2];
        for (int i = 0; i < n; ++i)
            if (i != p && !ban.count(i))
                sets[i % 2].insert(i);
        sets[0].insert(n);
        sets[1].insert(n); // 哨兵

        vector<int> ans(n, -1);
        vector<int> q = {p};
        for (int step = 0; !q.empty(); ++step)
        {
            vector<int> nq;
            for (int i : q)
            {
                ans[i] = step;
                //  int offsetMin = max(i + k - 1 - n, 0);
                //  int offsetMax = min(i, k - 1);
                // int mn = i + k - 1 - 2 * offsetMax;
                // int mx = i + k - 1 - 2 * offsetMin;
                // 从 mn 到 mx 的所有位置都可以翻转到
                int mn = max(i - k + 1, k - i - 1);
                int mx = min(i + k - 1, n * 2 - k - i - 1);
                auto &s = sets[mn % 2];
                for (auto it = s.lower_bound(mn); *it <= mx; it = s.erase(it))
                    nq.push_back(*it);
            }
            q = move(nq);
        }
        return ans;
    }
};

// class Solution
// {
// public:
//     vector<int> minReverseOperations(int n, int p, vector<int> &banned, int k)
//     {
//         vector<bool> onehotBanned(n, false);
//         for (int b : banned)
//         {
//             onehotBanned[b] = true;
//         }
//         vector<int> visited(n, -1);
//         queue<int> Q;
//         Q.push(p);
//         visited[p] = 0;
//         while (!Q.empty())
//         {
//             int x = Q.front();
//             int nvx = visited[x] + 1;
//             Q.pop();
//             int offsetMin = max(x + k - 1 - n, 0);
//             int offsetMax = min(x, k - 1);
//             if (offsetMin > offsetMax)
//             {
//                 continue;
//             }
//             for (int offset = offsetMin; offset <= offsetMax; ++offset)
//             {
//                 int l = x - offset;
//                 int r = l + k - 1;
//                 int to = r - offset;
//                 if (visited[to] == -1 && !onehotBanned[to])
//                 {
//                     Q.push(to);
//                     visited[to] = nvx;
//                 }
//             }
//         }
//         return visited;
//     }
// };

int main(int argc, char const *argv[])
{
    Solution s;
    int n = 100000, p = 58425, k = 21719;
    vector<int> banned({48107, 83267, 98246, 79324, 47564, 32824, 50062, 3163, 5928, 58999, 35436, 72022, 84403, 13718, 41447, 22269, 46047, 9292, 46138, 11920, 7153, 12697, 94130, 43505, 91061, 11773, 40906, 24155, 40621, 85181, 16563, 86268, 44601, 93243, 51062, 17951, 87910, 18520, 74331, 77129, 44825, 79673, 30802, 1243, 66815, 94672, 58350, 33563, 90378, 98307, 4784, 28722, 89910, 73821, 92835, 13852, 34555, 27560, 3709, 30149, 94333, 24754, 84759, 81068, 6833, 9763, 81164, 20386, 35061, 82774, 40140, 38119, 56255, 69206, 71713, 73719, 42465, 55279, 60354, 85775, 66105, 97046, 58139, 49148, 5567, 82305, 43480, 77090, 91251, 39903, 90397, 45568, 79632, 80396, 46377, 12780, 85315, 18724, 34165, 28110, 63467, 3052, 87723, 82608, 57019, 9339, 2259, 25548, 7111, 54361, 39076, 84068, 45362, 61181, 75906, 75990, 96739, 4621, 15581, 44082, 11799, 46809, 93490, 73453, 55892, 9389, 55404, 53970, 19315, 96524, 51943, 11414, 88069, 62264, 47411, 2601, 75219, 98584, 70225, 50052, 27826, 56912, 27921, 4078, 66788, 48570, 32313, 58692, 77162, 56333, 34142, 27138, 76185, 2722, 29113, 28290, 25086, 73007, 52291, 68356, 63461, 90782, 69160, 79218, 36495, 65859, 20700, 49195, 80204, 92494, 59089, 18427, 18732, 43850, 91685, 65383, 38800, 13897, 98544, 44544, 79872, 72831, 76502, 33469, 48467, 45887, 53547, 98121, 20850, 76381, 63238, 25632, 60892, 9613, 12744, 206, 2739, 85591, 80956, 45994, 13633, 85041, 19227, 55793, 33752, 16419, 33995, 99509, 29550, 85459, 33696, 4560, 84186, 81549, 24868, 41531, 34186, 97490, 42692, 37688, 97711, 84362, 86028, 88723, 30166, 81438, 86430, 56049, 70671, 25141, 29003, 20656, 89790, 88013, 14731, 11938, 69586, 4123, 14720, 40372, 87315, 58756, 65568, 34870, 8694, 59514, 62174, 42072, 84648, 23816, 73288, 38839, 5049, 18131, 28204, 86699, 35878, 75474, 18832, 15418, 322, 91955, 18009, 14638, 33546, 30030, 8552, 35710, 48030, 17307, 42870, 39880, 55073, 56451, 92161, 92829, 68689, 41442, 99155, 85696, 58736, 52443, 84993, 43608, 13051, 69072, 39606, 31899, 93088, 81781, 10238, 91565, 84703, 64649, 34482, 78079, 77772, 83458, 4832, 46501, 42934, 90420, 76802, 7028, 24427, 85436, 66083, 82838, 74185, 90790, 68317, 67774, 8409, 95174, 96178, 39839, 6260, 37769, 54188, 60349, 81073, 3913, 63864, 93932, 20910, 81308, 34863, 98519, 95830, 47742, 64879, 36964, 97167, 85593, 96321, 39250, 24995, 85911, 60013, 87440, 22966, 92948, 11384, 51068, 55666, 18049, 26661, 54504, 82956, 59803, 56060, 6494, 29774, 36682, 73110, 65772, 57078, 89782, 15928, 135, 73473, 95553, 22714, 85805, 50267, 84489, 66226, 31131, 87894, 74681, 65606, 21199, 66638, 62700, 81546, 82222, 44383, 18643, 58556, 43403, 7975, 6417, 31340, 74596, 56865, 27453, 41715, 60598, 58452, 84863, 44525, 82087, 42274, 16929, 70921, 84840, 79710, 53701, 7362, 44296, 82946, 75161, 75970, 21441, 41806, 76431, 56309, 44729, 69031, 26741, 53324, 99381, 19065, 21071, 22860, 811, 84908, 74544, 2156, 8761, 15855, 26808, 37548, 56618, 46254, 26923, 33961, 31304, 74517, 33840, 67955, 24197, 78019, 1998, 57547, 46970, 83937, 27484, 16594, 60852, 63697, 22294, 69391, 37811, 58769, 675, 85826, 63606, 78859, 60362, 86880, 31522, 42225, 90487, 85840, 92151, 94578, 93888, 16497, 37102, 7431, 51685, 8940, 69643, 56877, 84111, 61227, 77259, 32689, 97235, 49271, 65485, 86563, 97254, 98988, 16304, 89228, 37441, 20741, 87985, 67411, 71140, 54055, 58589, 64635, 87274, 23692, 44764, 18867, 8177, 72250, 10625, 2552, 83542, 34518, 44152, 28019, 34784, 9279, 31086, 50589, 70797, 72366, 98756, 24207, 9043, 49061, 28828, 60482, 31214, 26706, 86270, 55315, 26238, 25525, 10461, 98137, 54186, 20597, 99089, 96379, 22516, 27096, 53755, 28185, 88619, 86616, 44413, 97265, 57786, 42599, 59619, 20717, 87483, 37798, 72612, 3316, 90137, 98357, 95488, 56042, 41834, 20962, 18487, 17681, 96719, 10266, 23536, 92936, 58036, 78682, 85286, 27518, 48260, 32008, 93442, 95036, 65538, 84452, 58156, 48454, 25050, 99126, 65714, 30396, 68239, 27757, 4387, 96201, 19414, 98896, 92544, 76535, 28058, 44603, 98352, 29979, 25810, 15551, 27125, 7676, 90960, 31364, 66291, 89248, 34007, 53042, 3062, 37241, 60558, 19018, 84284, 4729, 88279, 43371, 25929, 71074, 80755, 10042, 5583, 32016, 58993, 32529, 80276, 12843, 69937, 30439, 16625, 30783, 7212, 13709, 91544, 82957, 70745, 70068, 82551, 18683, 58847, 4800, 65649, 91930, 89428, 33320, 5496, 72918, 85116, 50730, 93414, 6324, 90199, 99659, 93466, 27128, 36003, 75769, 12618, 70862, 76301, 68457, 21678, 9549, 38503, 6192, 18770, 17652, 58494, 41205, 93873, 77897, 8181, 45200, 92941, 43269, 45998, 2206, 76314, 8081, 24414, 28293, 6689, 46535, 26435, 90138, 71461, 67583, 24406, 96510, 85652, 56100, 26724, 60616, 35079, 68877, 41941, 93872, 68828, 13985, 92613, 87249, 15630, 51353, 39823, 87571, 3346, 33228, 71273, 20565, 82961, 82570, 16883, 30464, 68989, 40702, 78529, 96053, 11818, 89685, 95337, 62724, 98356, 54623, 15765, 612, 39211, 43186, 56633, 23041, 98628, 7800, 57996, 75096, 24909, 51704, 36891, 62846, 81562, 98391, 16570, 22571, 56965, 55685, 15613, 15935, 59289, 19749, 19975, 50038, 61672, 7807, 25379, 39163, 76840, 11512, 82410, 19330, 68663, 83256, 54505, 25503, 63726, 49719, 53498, 8006, 75373, 97206, 72244, 91287, 2326, 5643, 44445, 36255, 4525, 71950, 66429, 62786, 73094, 12660, 34335, 60671, 41881, 48206, 79833, 67215, 11998, 26126, 84080, 70451, 80256, 72769, 77422, 44217, 46838, 67045, 72734, 94937, 67221, 11662, 19126, 61074, 44455, 317, 61118, 37559, 55166, 39570, 85783, 6345, 60658, 88554, 96446, 80944, 5675, 69948, 10234, 7016, 72357, 62833, 64877, 84384, 57338, 44720, 88945, 89193, 65527, 79973, 91340, 34451, 28998, 47911, 79639, 9672, 73430, 35592, 34460, 14705, 87980, 41037, 43366, 71041, 8548, 63526, 75232, 3868, 33980, 46819, 29188, 71213, 70163, 20626, 77615, 9781, 231, 39046, 95941, 30964, 30223, 63084, 22864, 69359, 81281, 71223, 85620, 28555, 29437, 99903, 36540, 81985, 12032, 96661, 95855, 10319, 66706, 58265, 50824, 20035, 70721, 50482, 54432, 80553, 70847, 21781, 86677, 53512, 64797, 76828, 78985, 11654, 69431, 14315, 35239, 48786, 88444, 82694, 76226, 88426, 84787, 86986, 86971, 15420, 14104, 18017, 86076, 19064, 37157, 2150, 27848, 76463, 4098, 89990, 27633, 26107, 69437, 80654, 93612, 30188, 93585, 90256, 83753, 82239, 67784, 74170, 16916, 13232, 21705, 85313, 69867, 40075, 65186, 78509, 61394, 6290, 85496, 38111, 67359, 31544, 49392, 34986, 34177, 7793, 94691, 96916, 85999, 64209, 65663, 71831, 87819, 95272, 25359, 89429, 99908, 49496, 67337, 20636, 5782, 62612, 76551, 94347, 85476, 79408, 65636, 7618, 12941, 80815, 61943, 79836, 12983, 40745, 94447, 85651, 65939, 83075, 17977, 10023, 65932, 46306, 87614, 75351, 13778, 80712, 97087, 55019, 16106, 37251, 82387, 17746, 84998, 19253, 35967, 80043, 65710, 24080, 41087, 12487, 44074, 64970, 83908, 70292, 35216, 67213, 44164, 75477, 78926, 39532, 64240, 77516, 73957, 89182, 46564, 16353, 74773, 71081, 80855, 22604, 34926, 12866, 23761, 26687, 11369, 54079, 64889, 76497, 34485, 87949, 38309, 54789, 94856, 10636, 58527, 75251, 39109, 14743, 61405, 11095, 34021, 38334, 45509, 36129, 6589, 47032, 71370, 605, 28195, 64363, 40852, 56176, 84029, 68766, 21837, 75919, 42975, 69988, 96196, 95371, 62610, 87471, 11131, 34760, 58109, 52884, 10719, 78266, 45294, 63727, 97787, 97436, 46340, 18845, 85874, 45932, 83863, 69140, 48383, 27507, 65547, 14776, 20526, 16489, 42638, 4884, 61022, 35294, 50765, 99520, 60165, 97685, 47690, 52435, 36945, 436, 87468, 79385, 85752, 55678, 83218, 2422, 29060, 39585, 38855, 45058, 73027, 59117, 46134, 27911, 35565, 63563, 504, 37392, 64823, 91916, 73280, 77632, 97883, 37484, 73541, 52868, 93329, 21656, 28319, 39013, 64448, 6425, 76913, 25721, 48945, 52164, 56077, 801, 8235, 63005, 30539, 55050, 52250, 62513, 53399, 52676, 90084, 95468, 53389, 29620, 59594, 98088, 5854, 28457, 88732, 74134, 98727, 12534, 95486, 60146, 60339, 11800, 83396, 32359, 69929, 71521, 78865, 43414, 2212, 64476, 6806, 13264, 48312, 96156, 71685, 72776, 75023, 42509, 82309, 78437, 71662, 96529, 38380, 90995, 11595, 22207, 76853, 64590, 60569, 39701, 24058, 55631, 64680, 93797, 13401, 73297, 98021, 41790, 84971, 11759, 51478, 9301, 70319, 69292, 68969, 17633, 26708, 37588, 4153, 24994, 57012, 53299, 59681, 94248, 72819, 7450, 79123, 22459, 88060, 13930, 93555, 16911, 24531, 76213, 41629, 57624, 23596, 95011, 11082, 33123, 61506, 56256, 93847, 54216, 42356, 24603, 35013, 56154, 72658, 76762, 8160, 15596, 91076, 96434, 1003, 87428, 12926, 27980, 56008, 96908, 99473, 48053, 88469, 27187, 78337, 16028, 88383, 89500, 63260, 32935, 79154, 5369, 10091, 15501, 88854, 86367, 98426, 82635, 48366, 27262, 5005, 29181, 39563, 69015, 40956, 72682, 11941, 39227, 8610, 95639, 58334, 45605, 28839, 45985, 65953, 42727, 28505, 89058, 74111, 35057, 61337, 40212, 11836, 65777, 76844, 92255, 28415, 46910, 17600, 58089, 68095, 33773, 56718, 97153, 55266, 45360, 93346, 70699, 79887, 21728, 56571, 57420, 57361, 37976, 58829, 20874, 85464, 40206, 48304, 11495, 48237, 84372, 10467, 77310, 83284, 40643, 92283, 35665, 92370, 27349, 73971, 72245, 26956, 20114, 37529, 10383, 80906, 20319, 81280, 75045, 43459, 35876, 88237, 83480, 90345, 53766, 82976, 67891, 63594, 82562, 97389, 48394, 81757, 67631, 41480, 10503, 89794, 67603, 43727, 44018, 62078, 28477, 88101, 36508, 57942, 29025, 45898, 34042, 97143, 62599, 28389, 97623, 63924, 7202, 69337, 21720, 34603, 884, 94741, 8519, 43802, 53106, 48844, 96392, 56324, 78705, 7308, 93626, 18016, 56268, 37660, 2486, 35231, 34090, 65531, 57840, 23104, 48665, 13840, 92748, 95646, 13370, 47231, 63051, 99440, 51569, 23830, 45324, 39730, 62737, 71728, 68121, 36468, 58432, 19780, 3898, 19991, 5949, 22402, 32243, 66936, 63746, 38751, 48785, 13415, 67399, 32916, 46974, 25550, 81963, 31170, 81623, 83364, 55000, 40778, 17157, 69904, 67029, 32603, 23327, 91936, 25627, 12707, 79854, 35720, 9322, 27930, 35280, 4792, 12624, 21614, 32145, 28046, 59469, 97501, 56231, 62920, 13861, 96855, 61305, 24700, 71445, 65195, 40636, 66753, 10007, 76019, 24767, 82849, 78433, 61112, 63460, 63135, 21254, 94047, 41066, 89951, 84315, 99539, 70043, 75107, 4291, 68048, 52113, 88473, 44244, 22019, 22710, 9082, 10911, 47477, 97169, 78568, 48631, 22851, 83291, 75071, 92335, 5341, 51164, 26558, 12614, 69115, 64504, 56429, 51892, 16266, 96722, 68327, 76927, 30013, 38655, 88228, 10272, 62945, 88916, 43253, 51447, 90155, 24677, 74181, 97560, 50163, 46898, 76174, 4704, 77315, 25797, 10343, 91511, 32856, 58603, 85564, 65221, 95502, 58021, 68777, 49055, 98332, 6504, 98255, 74535, 99942, 156, 41381, 59300, 91094, 26861, 23985, 86124, 56453, 56911, 46369, 55366, 62285, 33462, 83138, 895, 41364, 94419, 52494, 16923, 72775, 26160, 59112, 65713, 59830, 52747, 81238, 51500, 54590, 97121, 46012, 66210, 21796, 34104, 1012, 20514, 45554, 98725, 2820, 33891, 36302, 75480, 10973, 99678, 82472, 63916, 43893, 28945, 82379, 26622, 7632, 27919, 9376, 39300, 26717, 33485, 13836, 39664, 55952, 91342, 63006, 21145, 83853, 6800, 53293, 91941, 51626, 5600, 88870, 43387, 5391, 80979, 77139, 50677, 73784, 47956, 86101, 67570, 6699, 50303, 36278, 50791, 40971, 33875, 60943, 61176, 69649, 74427, 70322, 91273, 98862, 18126, 8290, 31505, 57359, 4848, 99746, 36503, 64941, 33580, 90384, 99610, 67813, 29613, 40684, 34768, 11614, 93024, 57818, 68791, 57470, 67508, 91695, 74545, 42181, 55720, 32713, 5312, 26349, 77654, 98773, 90016, 79567, 88233, 73085, 49512, 31789, 19944, 342, 45830, 98525, 34676, 68727, 24869, 68542, 44998, 26601, 95670, 37871, 65002, 3731, 19548, 91025, 52210, 7816, 34514, 72271, 72760, 17777, 58524, 96030, 57467, 60973, 4845, 50847, 65771, 45842, 92708, 72212, 8384, 247, 12881, 49290, 25504, 85894, 42665, 39992, 32656, 61412, 23460, 13396, 99283, 13009, 95969, 22989, 46597, 58028, 30394, 1649, 2270, 45024, 33649, 9069, 77217, 5916, 59210, 71960, 3301, 45556, 79, 43481, 22145, 9639, 94314, 53686, 38110, 83009, 94267, 10299, 34089, 54180, 77508, 52405, 56483, 99694, 5502, 25614, 4360, 7313, 75449, 38831, 90936, 93846, 54599, 53500, 13286, 83813, 24167, 47084, 92418, 49249, 98375, 21764, 57718, 96036, 35826, 69658, 13328, 54565, 10907, 70371, 55422, 60184, 26114, 38165, 83941, 35398, 13414, 63903, 92785, 86038, 77093, 48736, 72516, 94202, 35391, 15252, 60612, 96744, 99081, 31590, 58326, 87253, 33286, 54516, 46840, 52763, 44154, 78022, 19392, 42294, 66383, 34158, 39450, 96623, 14178, 56305, 25042, 54826, 30099, 44305, 16587, 28309, 28799, 12105, 773, 82951, 28845, 64093, 29306, 47776, 78115, 58251, 10452, 15546, 32333, 45222, 13481, 4893, 17946, 20719, 84158, 56899, 74041, 21485, 56347, 16327, 47532, 14207, 66140, 90448, 70059, 77167, 31310, 64519, 99512, 57408, 30957, 23521, 78650, 21094, 9480, 78722, 36522, 33538, 64052, 93845, 15512, 28766, 35155, 88046, 27365, 52961, 48805, 96625, 16438, 35935, 30460, 8779, 43037, 84336, 3757, 62272, 99439, 25152, 17190, 1834, 47698, 67132, 85820, 70766, 22162, 1038, 52214, 2824, 19468, 16998, 39718, 88832, 27847, 16642, 28967, 15024, 14792, 53017, 42603, 69011, 92029, 18801, 76244, 87703, 761, 68167, 64254, 36360, 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69012, 15197, 66043, 5144, 99338, 62975, 22628, 59627, 18621, 79664, 24648, 7107, 86058, 27811, 40531, 37227, 79348, 24548, 17716, 74234, 67165, 80134, 37310, 78735, 32401, 68971, 7645, 26796, 11100, 71226, 52647, 62877, 38345, 44854, 70079, 90535, 62540, 50126, 15492, 86799, 86711, 24618, 60600, 38595, 7321, 181, 96012, 786, 57044, 90819, 46016, 60642, 84254, 69528, 54263, 35666, 89042, 76690, 18023, 94809, 57652, 52185, 11901, 43055, 96600, 7806, 7113, 21380, 7108, 31500, 85842, 30640, 38765, 90593, 76236, 18225, 29487, 67332, 59350, 92186, 27261, 10978, 45177, 19171, 97204, 71309, 73030, 18682, 14802, 47004, 76107, 59455, 39904, 50510, 54661, 41015, 97050, 94779, 64354, 30116, 75981, 97546, 58661, 35724, 7075, 54535, 36335, 33955, 80382, 43936, 16585, 4204, 13361, 72772, 43703, 77306, 63900, 49106, 45519, 49294});
    vector<int> res = s.minReverseOperations(n, p, banned, k);
    for (int i = 0; i < res.size(); i++)
    {
        cout << res[i] << " ";
    }
    cout << endl;
    return 0;
}
